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Chapter 19: Problem 76

Indicate whether \(\Delta G\) increases, decreases, or does not change when the partial pressure of \(\mathrm{H}_{2}\) is increased in each of the following reactions: (a) $\mathrm{H}_{2}(g)+\mathrm{NiO}(s) \longrightarrow \mathrm{Ni}(s)+\mathrm{H}_{2} \mathrm{O}(g)$ (b) $\mathrm{H}_{2}(g)+\mathrm{S}(s) \longrightarrow \mathrm{H}_{2} \mathrm{~S}(g)$ (c) $\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$

Short Answer

Expert verified
For all three reactions (a) H2(g) + NiO(s) -> Ni(s) + H2O(g), (b) H2(g) + S(s) -> H2S(g), and (c) C(s) + H2O(g) -> CO(g) + H2(g), increasing the partial pressure of H2 leads to an increase in the Gibbs free energy (∆G).

Step by step solution

01

(a) Examine the reaction: H2(g) + NiO(s) -> Ni(s) + H2O(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2 and H2O since only those substances are in gaseous form. The relationship between Q and ∆G is given by the equation: \[ ∆G = ∆G^0 + RT\ln{Q}\] where ∆G is the Gibbs free energy, ∆G^0 is the standard Gibbs free energy, R is the gas constant, T is the temperature, and Q is the reaction quotient. Now, when the partial pressure of H2 increases, the reaction quotient (Q) also increases. According to the equation above, this means that ∆G will increase.
02

(b) Examine the reaction: H2(g) + S(s) -> H2S(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2 and H2S, since both substances are in gaseous form. The relationship between Q and ∆G remains the same as in the previous example. When the partial pressure of H2 increases, the reaction quotient (Q) also increases. Therefore, ∆G will increase for this reaction as well.
03

(c) Examine the reaction: C(s) + H2O(g) -> CO(g) + H2(g)

In this reaction, the reaction quotient (Q) depends on the partial pressures of H2O, CO, and H2; only C(s) in solid state doesn't affect Q. The relationship between Q and ∆G remains the same. When the partial pressure of H2 increases, the reaction quotient (Q) also increases. Thus, ∆G will also increase for this reaction. So, in summary, for all three reactions (a), (b), and (c), the Gibbs free energy (∆G) increases when the partial pressure of H2 is increased.

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Most popular questions from this chapter

(a) What is the difference between a state and a microstate of a system? (b) As a system goes from state A to state B, its entropy decreases. What can you say about the number of microstates corresponding to each state? (c) In a particular spontaneous process, the number of microstates available to the system decreases. What can you conclude about the sign of \(\Delta S\) surr?

Consider the following reaction between oxides of nitrogen: $$ \mathrm{NO}_{2}(g)+\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{NO}(g) $$ (a) Use data in Appendix \(C\) to predict how \(\Delta G\) for the reaction varies with increasing temperature. (b) Calculate \(\Delta G\) at \(800 \mathrm{~K}\), assuming that \(\Delta H^{\circ}\) and \(\Delta S^{\circ}\) do not change with temperature. Under standard conditions is the reaction spontaneous at $800 \mathrm{~K} ?\( (c) Calculate \)\Delta G\( at \)1000 \mathrm{~K}$. Is the reaction spontaneous under standard conditions at this temperature?

(a) What sign for \(\Delta S\) do you expect when the pressure on 0.600 mol of an ideal gas at \(350 \mathrm{~K}\) is increased isothermally from an initial pressure of \(76.0 \mathrm{kPa} ?(\mathbf{b})\) If the final pressure on the gas is \(121.6 \mathrm{kPa}\), calculate the entropy change for the process. (c) Do you need to specify the temperature to calculate the entropy change?

Using data from Appendix \(\mathrm{C}\), calculate the change in Gibbs free energy for each of the following reactions. In each case, indicate whether the reaction is spontaneous at \(298 \mathrm{~K}\) under standard conditions. (a) \(2 \mathrm{Ag}(s)+\mathrm{Cl}_{2}(g) \longrightarrow 2 \mathrm{AgCl}(s)\) (b) $\mathrm{P}_{4} \mathrm{O}_{10}(s)+16 \mathrm{H}_{2}(g) \longrightarrow 4 \mathrm{PH}_{3}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)$ (c) $\mathrm{CH}_{4}(g)+4 \mathrm{~F}_{2}(g) \longrightarrow \mathrm{CF}_{4}(g)+4 \mathrm{HF}(g)$ (d) $2 \mathrm{H}_{2} \mathrm{O}_{2}(l) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+\mathrm{O}_{2}(g)$

The element sodium (Na) melts at \(97.8^{\circ} \mathrm{C},\) and its molar enthalpy of fusion is $\Delta H_{\text {fus }}=2.60 \mathrm{~kJ} / \mathrm{mol}$. (a) When molten sodium solidifies to \(\mathrm{Na}(\mathrm{s})\), is \(\Delta S\) positive or negative? (b) Calculate the value of \(\Delta S\) when \(50.0 \mathrm{~g}\) of \(\mathrm{Na}(l)\) solidifies at \(97.8^{\circ} \mathrm{C}\).
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